Electronic apparatus with two quartz crystal oscillators utilizing different vibration modes

ABSTRACT

The electronic apparatus comprises a display portion and a quartz crystal oscillator at least, and said electronic apparatus comprises at least two quartz crystal oscillators. Also, each of two quartz crystal oscillators of the at least two oscillators comprises a quartz crystal oscillating circuit having an amplification circuit and a feedback circuit. The feedback circuit is constructed by a flexural mode, quartz crystal tuning fork resonator or a width-extensional mode quartz crystal resonator or a thickness shear mode quartz crystal resonator and for example, the quartz crystal tuning fork resonator comprising tuning fork tines and tuning fork base that are formed integrally, is shown with novel shape and electrode construction. Also, the quartz crystal tuning fork resonator, capable of vibrating in a fundamental mode and having a high frequency stability can be provided with a small series resistance and a high quality factor, even when the tuning fork resonator is miniaturized. This is accomplished by grooves, groove dimensions and electrode construction on the tuning fork tines and/or tuning fork base of the quartz crystal tuning fork resonator. In addition, from a relationship of an amplification rate and a feedback rate, the quartz crystal oscillator having an output signal of a frequency of the fundamental mode vibration for the quartz crystal tuning fork resonator can be provided with the high frequency stability.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of copending U.S. patentapplication Ser. No. 10/378,724 filed Mar. 4, 2003 now U.S. Pat. No.6,897,743 and claiming a priority date of Mar. 6, 2002.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an electronic apparatus comprising atleast a display portion and a quartz crystal oscillator.

2. Background Information

There are many electronic apparatuses comprising at least a displayportion and a quartz crystal oscillator. For example, cellular phones,wristwatches and pagers comprising a quartz crystal oscillator are wellknown. Recently, because of high stability for frequency,miniaturization and the light weight nature of these electronicapparatus, the need for an electronic apparatus comprising a smallerquartz crystal oscillator with a high frequency stability has arisen.For example, the quartz crystal oscillator with a quartz crystal tuningfork resonator, which is capable of vibrating in a flexural mode, iswidely used as a time standard in an electronic apparatus such ascellular phones, wristwatches and pagers. Similar to this, the same needhas also arisen for an electronic apparatus comprising awidth-extensional mode quartz crystal resonator and a thickness shearmode quartz crystal resonator.

Heretofore, however, it has been impossible to obtain an electronicapparatus comprising a smaller quartz crystal oscillator with aconventional miniaturized quartz crystal tuning fork resonator, capableof vibrating in a flexural mode, and having a high frequency stability,a small series resistance and a high quality factor. When miniaturized,the conventional quartz crystal tuning fork resonator capable ofvibrating in a flexural mode, as shown in FIG. 10 (which has electrodeson the obverse faces 203, 207, reverse faces 204, 208 and the four sides205, 206, 209, 210 of each tuning fork tine, as also shown in FIG. 11—across-sectional view of tuning fork tines of FIG. 10), it has a smallerelectromechanical transformation efficiency because the resonator shapeand the electrode construction provide a small electric field (i.e. Exbecomes small), as a result of which the resonator has a low frequencystability, a large series resistance and a reduced quality factor. InFIG. 10, a conventional tuning fork resonator 200 is shown with tuningfork tines 201, 202 and a tuning fork base 230.

Moreover, for example, Japanese Patent Nos. P56-65517 and P2000-223992Aand International Patent No. WO 00/44092 were published and teachgrooves and electrodes constructed at tuning fork tines of a flexuralmode, tuning fork, quartz crystal resonator. However, they teach nothingabout a quartz crystal oscillator of the present invention having novelshape, novel electrode construction and figure of merit M for a quartzcrystal tuning fork resonator, capable of vibrating in a flexural modeand about a relationship of an amplification circuit and a feedbackcircuit which construct a quartz crystal oscillating circuit.

Additionally, for example, there has been a big problem in theconventional quartz crystal oscillator with the conventional quartzcrystal tuning fork resonator, such that a fundamental mode vibration ofthe resonator jumps to a second overtone mode vibration by shock orvibration.

In addition, as a quartz crystal resonator of the prior art, a NS-GT cutcoupling quartz crystal resonator which vibrates in the coupledwidth-extensional mode and length-extensional mode is well known. FIG.12 a and FIG. 12 b show a top view and a side view of the conventionalNS-GT cut coupling quartz crystal resonator. In FIG. 12 a and FIG. 12 b,the resonator 300 comprises a vibrational portion 301, connectingportions 303, 306 and supporting portions 304, 307. The supportingportions 304 and 307 include respective mounting portions 305 and 308.

Likewise, as shown in FIG. 12 a and FIG. 12 b, electrodes 302 and 311are disposed on the upper and lower faces of the vibrational portion301, the electrode 302 extends to the mounting portion 305 through theconnecting portion 303, while the electrode 311 extends to the mountingportion 308 through the connecting portion 306. The electrodes 302 and311 have opposite electrical polarities, and two electrode terminals areconstructed.

Now, when an alternating current(AC) voltage is applied between theelectrodes 302 and 311, an electric field E_(t) occurs alternately inthe thickness T direction, as shown by arrow signs of the solid andbroken lines in FIG. 12 b. As a result, the coupled width-extensionalmode and the length-extensional mode whose frequencies are inverselyproportional to width W and length L of the vibrational portion,respectively, can be excited at the same time, and the NS-GT cutcoupling resonator coupled in inverse phase is provided. Theabove-mentioned resonator is formed integrally by a chemical etchingprocess.

Furthermore, the lager the area of vibrational portion for the NS-GT cutresonator becomes (low frequency), the smaller series resistance R₁becomes and the larger a quality factor Q becomes. Also, the NS-GT cutresonator with excellent frequency temperature behavior is determined bya dimensional ratio W/L, and which has a value of 0.95 approximately. Inorder to get a frequency higher than 4 MHz, it is necessary to decreasethe area of the vibrational portion for the resonator.

According to the miniaturization and the light weight nature of anelectronic apparatus comprising a quartz crystal oscillator with anoutput signal of a frequency higher than 4 MHz, a miniature quartzcrystal oscillator comprising a NS-GT cut resonator with the higherfrequency is also required with a small series resistance R₁ and highquality factor Q.

It has been, however, impossible to provide an electronic apparatuscomprising a miniature quartz crystal oscillator having a NS-GT cutresonator with a frequency higher than about 4 MHz with a small seriesresistance R₁ and a high quality factor Q because the area ofvibrational portion for the resonator becomes very small to get thehigher frequency, and more an electromechanical transformationefficiency becomes very small, so that a series resistance R₁ becomeslarge and a quality factor Q also becomes small.

It is, therefore, a general object of the present invention to provideembodiments of an electronic apparatus and a quartz crystal oscillator,which constructs an electronic apparatus of the present invention,comprising a quartz crystal oscillating circuit with a flexural mode,quartz crystal tuning fork resonator, capable of vibrating in afundamental mode, and having a high frequency stability, a small seriesresistance and a high quality factor, or embodiments of a quartz crystaloscillator, which also constructs an electronic apparatus of the presentinvention, comprising a quartz crystal oscillating circuit with awidth-extensional mode quartz crystal resonator having a frequencyhigher than 4 MHz, a small series resistance and a high quality factor,which overcome or at least mitigate one or more of the above problems.

SUMMARY OF THE INVENTION

The present invention relates to an electronic apparatus comprising atleast a display portion and a quartz crystal oscillator. The quartzcrystal oscillator comprises a quartz crystal oscillating circuit havingan amplification circuit and a feedback circuit. The quartz crystaloscillating circuit comprises a flexural mode, quartz crystal tuningfork resonator capable of vibrating in a fundamental mode and having ahigh frequency stability for the fundamental mode vibration, and asuppressed second overtone mode vibration of the flexural mode.

In another embodiment, the quartz crystal oscillator comprises a quartzcrystal oscillating circuit comprising a width-extensional mode quartzcrystal resonator. The quartz crystal oscillators are, therefore,available for the electronic apparatus requiring miniaturized and lowpriced quartz crystal oscillators with high time accuracy and shockproof.

It is an object of the present invention to provide an electronicapparatus comprising at least a display portion and a quartz crystaloscillator.

It is an another object of the present invention to provide anelectronic apparatus comprising a quartz crystal oscillator comprising aquartz crystal oscillating circuit with a miniature quartz crystaltuning fork resonator, capable of vibrating in a flexural mode, andhaving a high frequency stability, a small series resistance R₁ and ahigh quality factor Q₁, whose frequency for a fundamental mode vibrationis within a range of 10 kHz to 200 kHz.

It is a further object of the present invention to provide an electronicapparatus comprising a quartz crystal oscillator comprising a quartzcrystal oscillating circuit with a flexural mode, quartz crystal tuningfork resonator, capable of vibrating in a fundamental mode, and having ahigh frequency stability which gives a high time accuracy.

It is a still further object of the present invention to provide anelectronic apparatus comprising a quartz crystal oscillator comprising aquartz crystal oscillating circuit with a width-extensional mode quartzcrystal resonator or a thickness shear mode quartz crystal resonator.

According to one aspect of the present invention, there is provided anelectronic apparatus comprising a display portion and a quartz crystaloscillator at least, and the electronic apparatus comprises at least twoquartz crystal oscillators and each of two quartz crystal oscillators ofthe at least two quartz crystal oscillators comprises: a quartz crystaloscillating circuit comprising; one quartz crystal resonator of at leasttwo quartz crystal resonators which are capable of vibrating in adifferent mode, respectively, in addition, the each quartz crystaloscillator comprises the quartz crystal oscillating circuit comprisingan amplification circuit comprising an amplifier at least and a feedbackcircuit comprising the one quartz crystal resonator and capacitors atleast, and the one quartz crystal resonator is a quartz crystal tuningfork resonator capable of vibrating in a flexural mode. Especially, thequartz crystal tuning fork resonator is capable of vibrating in afundamental mode and comprises; tuning fork tines each of which has alength, a width and a thickness and the length greater than the widthand the thickness, and a tuning fork base, said tuning fork tines andsaid tuning fork base that are formed integrally, grooves provided atsaid tuning fork tines, and electrodes disposed opposite each otherinside the grooves and on sides of said tuning fork tines so that theelectrodes disposed opposite each other are of opposite electricalpolarity and said tuning fork tines are capable of vibrating in inversephase.

According to a second aspect of the present invention there is providedan electronic apparatus comprising a display portion and a quartzcrystal oscillator at least, and the electronic apparatus comprises atleast two quartz crystal oscillators and each of two quartz crystaloscillators of the at least two quartz crystal oscillators comprises: aquartz crystal oscillating circuit comprising; one quartz crystalresonator of at least two quartz crystal resonators which are capable ofvibrating in a different mode, respectively, in addition, the eachquartz crystal oscillator comprises the quartz crystal oscillatingcircuit comprising an amplification circuit comprising an amplifier atleast and a feedback circuit comprising the one quartz crystal resonatorand capacitors at least, and the one quartz crystal resonator is awidth-extensional mode quartz crystal resonator capable of vibrating ina width-extensional mode or a thickness shear mode quartz crystalresonator capable of vibrating in a thickness shear mode.

Embodiments of the present invention use grooves and an electrodeconstruction arranged on tuning fork tines and/or a tuning fork base ofa flexural mode, quartz crystal tuning fork resonator.

Preferably, the tuning fork resonator has grooves including the centralline of the central portions for each tuning fork tine and theelectrodes disposed inside the grooves and disposed on the sides of eachtuning fork tine, and the grooves and the electrodes are constructed sothat figure of merit M₁ of a fundamental mode vibration is larger thanfigure of merit M₂ of a second overtone mode vibration.

Preferably, the quartz crystal oscillator with the tuning fork resonatoris constructed so that a ratio of an amplification rate α₁ of thefundamental mode vibration and an amplification rate α₂ of the secondovertone mode vibration of said amplification circuit is larger thanthat of a feedback rate β₂ of the second overtone mode vibration and afeedback rate β₁ of the fundamental mode vibration of said feedbackcircuit, and a product of the amplification rate α₁ and the feedbackrate β₁ of the fundamental mode vibration is larger than 1.

Preferably, the quartz crystal oscillator with the tuning fork resonatoris constructed so that a ratio of an absolute value of negativeresistance, |−RL₁| of the fundamental mode vibration of saidamplification circuit and series resistance R₁ of the fundamental modevibration is larger than that of an absolute value of negativeresistance, |−RL₂| of the second overtone mode vibration of saidamplification circuit and series resistance R₂ of the second overtonemode vibration.

Preferably, the width-extensional mode quartz crystal resonatorcomprises a vibrational portion, connecting portions and supportingportions, which are formed integrally by a particle method.

The present invention will be more fully understood by referring to thefollowing detailed specification and claims taken in connection with theappended drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of an embodiment of an electronic apparatusof the present invention, and illustrating the diagram of a facsimileapparatus;

FIG. 2 shows a diagram of an embodiment of a quartz crystal oscillatingcircuit constructing a quartz crystal oscillator, which constructs anelectronic apparatus of the present invention;

FIG. 3 shows a diagram of the feedback circuit of FIG. 2;

FIG. 4 shows a general view of a flexural mode, quartz crystal tuningfork resonator constructing a quartz crystal oscillator, whichconstructs an electronic apparatus of the first embodiment of thepresent invention;

FIG. 5 shows a cross-sectional view of the tuning fork base along line5—5 of FIG. 4 illustrating an electrode construction;

FIG. 6 shows a plan view of a quartz crystal tuning fork resonator ofFIG. 4;

FIG. 7 a and FIG. 7 b show a top view and a side view of awidth-extensional mode quartz crystal resonator constructing a quartzcrystal oscillator, which constructs an electronic apparatus of thesecond embodiment of the present invention;

FIG. 8 shows a cross-sectional view of a quartz crystal unitconstructing a quartz crystal oscillator, which constructs an electronicapparatus of the third embodiment of the present invention;

FIG. 9 shows a cross-sectional view of a quartz crystal oscillator,which constructs an electronic apparatus of the fourth embodiment of thepresent invention;

FIG. 10 is a general view of the conventional flexural mode, quartzcrystal tuning fork resonator constructing a quartz crystal oscillatorof the prior art, which constructs the conventional electronicapparatus;

FIG. 11 is a cross-sectional view of the tuning fork tines of FIG. 10and illustrates an electrode construction; and

FIG. 12 a and FIG. 12 b show a top view and a side view of theconventional NS-GT cut coupling quartz crystal resonator constructing aquartz crystal oscillator of the prior art, which constructs theconventional electronic apparatus.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to the drawings, the embodiments of the present inventionwill be described in more detail.

FIG. 1 shows a block diagram of an embodiment of an electronic apparatusof the present invention, and illustrating the diagram of a facsimileapparatus. As is shown in FIG. 1, the apparatus generally comprises amodem, a phonetic circuit, a timepiece circuit, a printing portion, ataking portion, an operation portion and a display portion. In thisprinciple, perception and scanning of reflection light of lightprojected on manuscript in the taking portion are performed byCCD(Charge Coupled Device), in addition, light and shade of thereflection light are transformed into a digital signal, and the signalis modulated by the modem and is sent to a phone line(Communicationline). Also, in a receiving side, a received signal is demodulated bythe modem and is printed on a paper in the print portion bysynchronizing the received signal with a signal of a sending side.

As shown in FIG. 1, a quartz crystal resonator is used as a CPU clock ofthe control portion and the printing portion, and as a clock of thephonetic circuit and the modem, and as a time standard of the timepiece.Namely, the quartz crystal resonator constructs a quartz crystaloscillator and an output signal of the oscillator is used. For example,it is used as a signal to display time at the display portion. In orderto get the facsimile apparatus of this embodiment which operatesnormally, an accuracy output signal of the quartz crystal oscillator isrequired for the facsimile apparatus, which is one of the electronicapparatus of the present invention. Also, a digital display and ananalogue display are included in the display of the present invention.

In this embodiment, though the facsimile apparatus is shown as anexample of an electronic apparatus, the present invention is not limitedto this, namely, the present invention includes all electronic apparatuscomprising a quartz crystal oscillator, for example, a cellular phone,telephone, TV set, camera, video set, video camera, pagers, personalcomputer, printer, CD player, MD player, electronic musical instrument,car navigation, car electronics, timepiece, IC card and so forth.

FIG. 2 shows a diagram of an embodiment of a quartz crystal oscillatingcircuit constructing a quartz crystal oscillator, which constructs anelectronic apparatus of the present invention. The quartz crystaloscillating circuit 1 comprises an amplifier (CMOS Inverter) 2, afeedback resistor 4, drain resistor 7, capacitors 5, 6 and a flexuralmode, quartz crystal tuning fork resonator 3. Namely, the quartz crystaloscillating circuit 1 comprises an amplification circuit 8 having theamplifier 2 and the feedback resistor 4, and a feedback circuit 9 havingthe drain resistor 7, the capacitors 5, 6 and the resonator 3. Inaddition, an output signal of the oscillating circuit 1 comprising theresonator 3, capable of vibrating in a fundamental mode, is outputtedthrough a buffer circuit (not shown in FIG. 2) from an output side ofthe amplifier (CMOS Inverter).

In detail, a frequency of the fundamental mode vibration is outputtedthrough a buffer circuit as an output signal. According to the presentinvention, the frequency of the fundamental mode vibration is within arange of 10 kHz to 200 kHz. Also, the present invention includes adivided frequency of the output signal with the frequency of thefundamental modes vibration by a divided circuit. In more detail, theoscillator comprises the quartz crystal oscillating circuit and thebuffer circuit, in other words, the oscillating circuit comprises theamplification circuit and the feedback circuit, and the amplificationcircuit comprises the amplifier at least and the feedback circuitcomprises the flexural mode, quartz crystal tuning fork resonator andthe capacitors at least. Also, flexural mode, quartz crystal tuning forkresonators which are used in a quartz crystal oscillator will bedescribed in FIG. 4–FIG. 6 in detail.

FIG. 3 shows a diagram of the feedback circuit of FIG. 2. Now, whenangular frequency ω_(i) of the flexural mode, quartz crystal tuning forkresonator 3, capable of vibrating in a flexural mode, a resistance R_(d)of the drain resistor 7, capacitance C_(g), C_(d) of the capacitors 5,6, crystal impedance R_(ei) of the quartz crystal resonator 3, an inputvoltage V₁, and an output voltage V₂ are taken, a feedback rate β_(i) isdefined by β_(i)=|V₂|_(i)/V₁|_(i), where i shows vibration order, forexample, when i=1 and 2, they are for fundamental mode vibration andsecond overtone mode vibration.

In addition, load capacitance C_(L) is given byC_(L)=C_(g)C_(d)/(C_(g)+C_(d)), and when C_(g)=C_(d)=C_(gd) andRd>>R_(ei), the feedback rate β_(i) is given by β_(i)=1/(1+kC_(L) ²),where k is expressed by a function of ω_(i), R_(d) and R_(ei). Also,R_(ei) is approximately equal to series resistance R_(i).

Thus, it is easily understood from a relationship of the feedback rateβ_(i) and load capacitance C_(L) that the feedback rate of resonancefrequency for a fundamental mode vibration and an overtone modevibration becomes large, respectively, according to decrease of loadcapacitance C_(L). Therefore, when C_(L) has a small value, anoscillation of the overtone mode occurs very easily, instead of that ofthe fundamental mode. This is the reason why a maximum amplitude of theovertone mode vibration becomes smaller than that of the fundamentalmode vibration, and the oscillation of the overtone mode satisfies anamplitude condition and a phase condition simultaneously which are thecontinuous condition of an oscillation in an oscillating circuit.

As it is also one object of the present invention to provide a quartzcrystal oscillator having a flexural mode, quartz crystal tuning forkresonator, capable of vibrating in a fundamental mode and having a highfrequency stability (high time accuracy) of an output signal, and havingreduced electric current consumption, in this embodiment, loadcapacitance C_(L) is less than 10 pF to reduce electric currentconsumption. To get much reduced electric current consumption, C_(L) ispreferably less than 8 pF because electric current consumption isproportional to C_(L). Here, C_(L) does not include stray capacity of anoscillating circuit. Actually, there exists the stray capacity byconstructing the oscillating circuit. Therefore, in this embodiment,load capacitance C_(L) including the stray capacity by constructing thecircuit is less than 18 pF.

In addition, in order to suppress a second overtone mode vibration andto obtain a quartz crystal oscillator having an output signal of afrequency of a fundamental mode vibration, the oscillator is constructedso that it satisfies a relationship of α₁/α₂>β₂/β₁ and α₁β₁>1, where α₁and α₂ are an amplification rate of the fundamental mode vibration andthe second overtone mode vibration of an amplification circuit,respectively, and β₁ and β₂ are a feedback rate of the fundamental modevibration and the second overtone mode vibration of a feedback circuit,respectively.

In other words, the quartz crystal oscillator is constructed so that aratio of the amplification rate α₁ of the fundamental mode vibration andthe amplification rate α₂ of the second overtone mode vibration of theamplification circuit is larger than that of the feedback rate β₂ of thesecond overtone mode vibration and the feedback rate β₁ of thefundamental mode vibration of the feedback circuit, and a product of theamplification rate α₁ and the feedback rate β₁ of the fundamental modevibration is larger than 1. By constructing it like this, it can beprovided with reduced electric current consumption and the output signalof the frequency of the fundamental mode vibration because the secondovertone mode vibration can be suppressed. In addition, a description ofthe high frequency stability will be performed later.

Also, characteristics of the amplifier of the amplification circuitconstructing the quartz crystal oscillating circuit of this embodimentcan be expressed by negative resistance −RL_(i). For example, when i=1,negative resistance −RL₁ is for a fundamental mode vibration and wheni=2, negative resistance −RL₂ is for a second overtone mode vibration.In this embodiment, the quartz crystal oscillating circuit isconstructed so that a ratio of an absolute value of negative resistance,|−RL₁| of the fundamental mode vibration of the amplification circuitand series resistance R₁ of the fundamental mode vibration is largerthan that of an absolute value of negative resistance, |−RL₂| of thesecond overtone mode vibration of the amplification circuit and seriesresistance R₂ of the second overtone mode vibration. That is to say, theoscillating circuit is constructed so that it satisfies a relationshipof |−RL₁|/R₁>|−RL₂|/R₂. By constructing the oscillating circuit likethis, an oscillation of the second overtone mode can be suppressed, as aresult an output signal of a frequency of the fundamental mode vibrationcan be provided because an oscillation of the fundamental mode generateseasily in the oscillating circuit.

FIG. 4 shows a general view of a flexural mode quartz crystal tuningfork resonator 10 constructing a quartz crystal oscillator, whichconstructs an electronic apparatus of the first embodiment of thepresent invention and its coordinate system o-xyz. A cut angle θ, whichhas a typical value of 0° to 10°, is rotated from a Z-plateperpendicular to the z axis about the x axis. The quartz crystalresonator 10 comprises two tuning fork tines 20 and 26 and a tuning forkbase 40. The tines 20 and 26 have grooves 21 and 27 respectively, withthe grooves 21 and 27 extending into the base 40. In addition, the base40 has the additional grooves 32 and 36.

FIG. 5 show a cross-sectional view of the tuning fork base 40 for quartzcrystal resonator 10 along line 5—5 of FIG. 4. In FIG. 5, the shape ofthe electrode construction within the base 40 for the quartz crystalresonator of FIG. 4 is described in detail. The section of the base 40which couples to the tine 20 has the grooves 21 and 22 cut into theobverse and reverse faces of the base 40. Also, the section of the base40 which couples to the tine 26 has the grooves 27 and 28 cut into theobverse and reverse faces of the base 40. In addition to these grooves,the base 40 has the grooves 32 and 36 cut between the grooves 21 and 27,and also, the base 40 has the grooves 33 and 37 cut between the grooves22 and 28.

Furthermore, the grooves 21 and 22 have the first electrodes 23 and 24both of the same electrical polarity, the grooves 32 and 33 have thesecond electrodes 34 and 35 both of the same electrical polarity, thegrooves 36 and 37 have the third electrodes 38 and 39 both of the sameelectrical polarity, the grooves 27 and 28 have the fourth electrodes 29and 30 both of same electrical polarity and the sides of the base 40have the fifth and sixth electrodes 25 and 31, each of oppositeelectrical polarity. In more detail, the fifth, fourth, and secondelectrodes 25, 29, 30, 34 and 35 have the same electrical polarity,while the first, sixth and third electrodes 23, 24, 31, 38 and 39 havethe opposite electrical polarity to the others. Two electrode terminalsE–E′ are constructed. That is, the electrodes disposed inside thegrooves constructed opposite each other in the thickness (z axis)direction have the same electrical polarity. Also, the electrodesdisposed opposite each other across adjoining grooves have oppositeelectrical polarity.

In addition, the resonator has a thickness t of the tines or the tinesand the base, and a groove thickness t₁. It is needless to say that theelectrodes are disposed inside the grooves and on the sides of thetines. In this embodiment, the first electrodes 23 and 24 are disposedat the tine and the base, and also, the fourth electrodes 29 and 30 aredisposed at the tine and the base. In addition, the electrodes aredisposed on the sides of the tines opposite each other to the electrodesdisposed inside the grooves. Namely, the electrodes are disposedopposite each other inside the grooves and on the sides of the tuningfork tines so that the electrodes disposed opposite each other are ofopposite electrical polarity.

Now, when a direct voltage is applied between the electrode terminalsE–E′ (E terminal: plus, E′ terminal: minus), an electric field Ex occursin the arrow direction as shown in FIG. 5. As the electric field E_(x)occurs perpendicular to the electrodes disposed on the base, theelectric field E_(x) has a large value and a large distortion occurs atthe base, so that a flexural mode, quartz crystal tuning fork resonatoris obtained with a small series resistance R₁ and a high quality factorQ₁, even if it is miniaturized.

FIG. 6 shows a plan view of a quartz crystal tuning fork resonator 10 ofFIG. 4. In FIG. 6, the construction and the dimension of grooves 21, 27,32 and 36 are described in detail. The groove 21 is constructed toinclude a portion of the central line 41 of the tine 20, the groove 27is similarly constructed to include a portion of the central line 42 ofthe tine 26. The width W₂ of the grooves 21 and 27 (groove width W₂)which include a portion of the central lines 41 and 42 respectively, ispreferable because moment of inertia of the tines 20 and 26 becomeslarge and the tines can vibrate in a flexural mode very easily. As aresult, the quartz crystal resonator capable of vibrating in afundamental mode can be obtained with a small series resistance R₁ and ahigh quality factor Q₁.

In more detail, when part widths W₁, W₃ and groove width W₂ are taken,the tine width W of the tines 20 and 26 has a relationship ofW=W₁+W₂+W₃, and a part or all of at least one of the grooves isconstructed so that W₁≧W₃ or W₁<W₃. In addition, the groove width W₂ isconstructed so that W₂≧W₁, W₃. In this embodiment, also, the grooves areconstructed at the tines so that a ratio(W₂/W) of the groove width W₂and the tine width W is larger than 0.35 and less than 1, and aratio(t₁/t) of the groove thickness t₁ and the thickness t of the tines(tine thickness t) is less than 0.79, to obtain very large moment ofinertia of the tines. That is, the quartz crystal resonator, capable ofvibrating in the fundamental mode, and having a high frequency stabilitycan be provided with a small series resistance R₁, a high quality factorQ₁ and a small capacitance ratio r₁ because electromechanicaltransformation efficiency becomes large.

Likewise, length l₁ of the grooves 21 and 27 of the tines 20 and 26extends into the base 40 in this embodiment (which has a dimension ofthe length l₂ and the length l₃ of the grooves). Therefore, groovelength and length of the tines are given by (l₁–l₃) and (l–l₂), and aratio of (l₁–l₃) and (l–l₂) is within a range of 0.4 to 0.8 to get aflexural mode, quartz crystal resonator with series resistance R₁ of afundamental mode vibration smaller than series resistance R₂ of a secondovertone mode vibration

Furthermore, the total length l is determined by the frequencyrequirement and the size of the housing case. Also, to get a flexuralmode, quartz crystal resonator capable of vibrating in a fundamentalmode with suppression of the second overtone mode vibration which isunwanted mode vibration, there is a close relationship between thegroove length l₁ and the total length l. Namely, a ratio(l₁/l) of thegroove length l₁ and the total length l is within a range of 0.2 to 0.78because the quantity of charges which generate within the grooves and onthe sides of the tines or the tines and the base can be controlled bythe ratio, as a result, the second overtone mode vibration, which isunwanted mode vibration, can be suppressed substantially, andsimultaneously, a frequency stability of the fundamental mode vibrationgets high. Therefore, the flexural mode, quartz crystal tuning forkresonator, capable of vibrating easily in the fundamental mode andhaving the high frequency stability can be provided.

In more detail, series resistance R₁ of the fundamental mode vibrationbecomes smaller than series resistance R₂ of the second overtone modevibration. Namely, R₁<R₂, preferably, R₁<0.86R₂, therefore, a quartzcrystal oscillator comprising an amplifier(CMOS inverter), capacitors,resistors and a quartz crystal unit with the quartz crystal tuning forkresonator of this embodiment can be obtained, which is capable ofvibrating in the fundamental mode very easily. In addition, in thisembodiment the grooves 21 and 27 of the tines 20 and 26 extend into thebase 40 in series, but embodiment of the present invention includes aplurality of grooves divided into the length direction of the tines. Inaddition, the grooves may be constructed only at the tuning forktines(l₃=0).

In this embodiment, the groove length l₁ corresponds to electrode lengthdisposed inside the grooves, though the electrode is not shown in FIG.6, but, when the electrode length is less than the groove length, thelength l₁ is of the electrode length. Namely, the ratio(l₁/l) in thiscase is expressed by a ratio of electrode length l₁ of the grooves andthe total length l. In order to achieve the above-mentioned object, itmay be satisfied with at least one groove with the ratio constructed atthe obverse and reverse faces of each tine. As a result, the flexuralmode, quartz crystal tuning fork resonator, capable of vibrating veryeasily in the fundamental mode and having the high frequency stabilitycan be realized. Also, a fork portion of this embodiment has arectangular shape, but this invention is not limited to this, forexample, the fork portion may have a U shape.

In addition, a space of between the tuning fork tines is given by W₄,and in this embodiment, the space W₄ and the groove width W₂ areconstructed so that W₄≧W₂, and more, the space W₄ is within a range of0.05 mm to 0.35 mm and the width W₂ is within a range of 0.03 mm to 0.12mm because it is easy to form a tuning fork shape and grooves of thetines separately by a photo-lithographic process and an etching process,consequently, a frequency stability for a fundamental mode vibrationgets higher than that for a second overtone mode vibration. In thisembodiment, a quartz crystal wafer with the thickness t of 0.05 mm to0.12 mm is used.

In more detail, to obtain a flexural mode, quartz crystal tuning forkresonator with a high frequency stability which gives high timeaccuracy, it is necessary to obtain the resonator whose resonancefrequency is not influenced by shunt capacitance because quartz crystalis a piezoelectric material and the frequency stability is verydependent on the shunt capacitance. In order to decrease the influenceon the resonance frequency by the shunt capacitance, figure of meritM_(i) plays an important role. Namely, the figure of merit M_(i) thatexpresses inductive characteristics, electromechanical transformationefficiency and a quality factor of a flexural mode, quartz crystaltuning fork resonator, is defined by a ratio (Q_(i)/r_(i)) of a qualityfactor Q_(i) and capacitance ratio r_(I), namely, M_(i) is given byM_(i)=Q_(i)/r_(i), where i shows vibration order of a flexural mode,quartz crystal tuning fork resonator, and for example, when i=1 and 2,figures of merit M₁ and M₂ are for a fundamental mode vibration and asecond overtone mode vibration of the resonator, respectively.

Also, a frequency difference Δf of resonance frequency f_(s) ofmechanical series independent on the shunt capacitance and resonancefrequency f_(r) dependent on the shunt capacitance is inverselyproportional to the figure of merit M_(i). The larger the value M_(i)becomes, the smaller the difference Δf becomes. Namely, the influence onthe resonance frequency f_(r) by the shunt capacitance decreases becauseit is close to the resonance frequency f_(s). Accordingly, the largerthe M_(i) becomes, the higher the frequency stability of the flexuralmode, quartz crystal resonator becomes because the resonance frequencyf_(r) of the resonator is almost never dependent on the shuntcapacitance. Namely, the flexural mode, quartz crystal tuning forkresonator can be provided with a high time accuracy.

In detail, a quartz crystal tuning fork resonator capable of vibratingin a flexural mode can be obtained with figure of merit M₁ of afundamental mode vibration larger than figure of merit M₂ of a secondovertone mode vibration by the above-described tuning fork shape,grooves and dimensions. That is to say, M₁>M₂. As an example, whenresonance frequency of a flexural mode, quartz crystal tuning forkresonator is about 32.768 kHz for a fundamental mode vibration and theresonator has a value of W₂/W=0.5, t₁/t=0.34 and l₁/l=0.48, though thereis a distribution in production, the resonator has a value of M₁>65 andM₂<30, respectively.

Namely, the flexural mode, quartz crystal tuning fork resonator which iscapable of vibrating in the fundamental mode can be provided with highinductive characteristics, good electromechanical transformationefficiency (small capacitance ratio r₁ and small series resistance R₁)and a high quality factor. As a result, a frequency stability of thefundamental mode vibration becomes higher than that of the secondovertone mode vibration, and simultaneously, the second overtone modevibration can be suppressed because capacitance ratio r₂ and seriesresistance R₂ of the second overtone mode vibration become larger thancapacitance ratio r₁ and series resistance R₁ of the fundamental modevibration, respectively.

Therefore, the resonator capable of vibrating in the fundamental modevibration can be provided with a high time accuracy because it has thehigh frequency stability. Consequently, a quartz crystal oscillatorcomprising the flexural mode, quartz crystal tuning fork resonator ofthis embodiment outputs a frequency of the fundamental mode vibration asan output signal, and the frequency of the output signal has a very highstability, namely, an excellent time accuracy. In other words, thequartz crystal oscillator of this embodiment has a remarkable effectsuch that a frequency change by ageing becomes very small. Also, afrequency of a fundamental mode vibration of the present invention iswithin a range of 10 kHz to 200 kHz. Especially, 32.768 kHz is usedwidely, and for example, frequency adjustment of the resonator isperformed so that a frequency deviation is within a range of −100 PPM to+100 PPM. Therefore, the output signal is used as a clock signal todisplay time at a display portion of an electronic apparatus of thepresent invention.

By constructing the space W₄ of between the tines, and groove width W₂as described above, it is easy to form the tines and grooves which areprovided at the tines separately, namely, by a separate step. However,in order to form the tines and the grooves simultaneously, it isnecessary to obtain an optimum dimension of tine thickness t, groovewidth W₂, space W₄ of the tines and groove area S(=l₁×W₂). For example,when the tine thickness t is within a range of 0.06 mm to 0.15 mm, thegroove width W₂, the groove area S and the space W₄ are constructed sothat they are within a range of 0.02 mm to 0.08 mm, 0.023 mm² to0.098mm² and 0.05 mm to 0.35 mm, respectively. This is whycrystallographic characteristics of quartz crystal and/or a groove shapeare used and from the crystallographic characteristics and/or the grooveshape, the grooves and the tines are formed simultaneously, namely, by asimultaneous step using a photo-lithographic process and an etchingprocess. As an example of the groove shape, groove width W₂ is notconstant along the length direction of tuning fork tines or grooves aredivided into the length direction thereof.

In addition, groove length l₁ of the present invention is length ofgrooves constructed at tines so that the ratio(t₁/t) of the groovethickness t₁ and the tine thickness t is less than 0.79, and theratio(W₂/W) of the groove width W₂ and the tine width W is larger than0.35 and less than 1, when the grooves are constructed only at thetuning fork tines, and also, when the grooves constructed at the tuningfork tines extend into a base and at least one groove is constructedbetween the grooves extended into the tuning fork base, groove lengthl₁, of the present invention is length of grooves constructed at thetines and the base(groove length l₃).

Namely, when the grooves constructed at the tines extend into the baseand at least one groove is not constructed between the grooves extendedinto the base, the groove length l₁ of the present invention is lengthof grooves constructed at the tines. Also, when the grooves of the tinesare divided into the length direction thereof or connected via at leastone step portion, the groove length l₁ is total length of the lengthdirection satisfying the ratios(t₁/t) and (W₂/W) described above. Inaddition, the groove thickness t₁ of the present invention is thethinnest thickness of the grooves because quartz crystal is ananisotropic material and the groove thickness t₁ has a distribution whenthe grooves are formed by a chemical etching method.

In summary the embodiments shown within FIG. 4 to FIG. 6, the tines havefour grooves within the obverse and the reverse faces thereof andelectrodes provided inside the grooves as well as electrodes disposed onboth sides of the tines. The embodiments of the present invention,however, may have at least one groove within at least one surface of thetines and an electrode inside the at least one groove as well aselectrodes disposed on both sides of the tine. Also, it is provided thatthe first electrode inside the groove and the second electrodes on saidside of the tine next to said electrode are of opposite electricalpolarity.

FIG. 7 a and FIG. 7 b are a top view and a side view for awidth-extensional mode quartz crystal resonator constructing a quartzcrystal oscillator, which constructs an electronic apparatus of thesecond embodiment of the present invention. The resonator 62 comprisesvibrational portion 63, connecting portions 66, 69 and supportingportions 67, 80 including respective mounting portions 68, 81. Inaddition, the supporting portions 67 and 80 have respective holes 67 aand 80 a. Also, electrodes 64 and 65 are disposed opposite each other onupper and lower faces of the vibrational portion 63, the electrodes haveopposite electrical polarities. Namely, a pair of electrodes is disposedon the vibrational portion. In this case, a fundamental mode vibrationcan be excited easily.

In addition, the electrode 64 extends to the mounting portion 81 throughthe one connecting portion 69 and the electrode 65 extends to themounting portion 68 through the other connecting portion 66. In thisembodiment, the electrodes 64 and 65 disposed on the vibrational portion63 extend to the mounting portions of the different direction eachother. However, a resonator with the same characteristics as saidresonator can be obtained, even if the electrodes 64 and 65 extend tothe mounting portions of the same direction each other. The resonator inthis embodiment is mounted on fixing portions of a case or a lid at themounting portions 68 and 81 by conductive adhesives or solder.

With respect to a cutting angle of the width-extensional mode quartzcrystal resonator, it is shown here. First, a quartz crystal plateperpendicular to x axis, so called, X plate quartz crystal is taken.Width W₀, length L₀ and thickness T₀ which are each dimension of the Xplate quartz crystal correspond to the respective directions of y, z andx axes.

Next, this X plate quartz crystal is, first, rotated with an angle θ_(x)of −25° to +25 about the x axis, and second, rotated with an angle θ_(y)of −30° to +30° about y′ axis which is the new axis of the y axis. Inthis case, the new axis of the x axis changes to x′ axis and the newaxis of the z axis changes to z″ axis because the z axis is rotatedtwice about two axes. the width-extensional mode quartz crystalresonator of the present invention is formed from the quartz crystalplate with the rotation angles.

In other words, according to an expression of IEEE notation, a cuttingangle of the width-extensional mode quartz crystal resonator of thepresent invention can be expressed by XZtw(−25°–+25°)/(−30°–+30°). Also,when a turn over temperature point T_(p) is taken in a vicinity of roomtemperature, a cutting angle of the width-extensional mode quartzcrystal resonator may be within a range of XZt(−12°–−13.5°) orXZt(−18.5°–−19.8°) or XZtw(−13°–−18°)/±(+0.5°–+30°). Namely, said threekinds of cutting angles in this embodiment is in the same direction asthe cutting angle of the DT cut quartz crystal resonator, which isformed from a rotated Y-plate about the x axis whose Y-plate isperpendicular to the y axis.

Moreover, the vibrational portion 63 has a dimension of width W₀, lengthL₀ and thickness Z₀, also, width W₀, length L₀ and thickness T₀correspond to y′, z″ and x′ axes, respectively. That is, the electrodes64 and 65 are disposed on the upper and lower faces of the vibrationalportion 63 perpendicular to the x′ axis.

In addition, the vibrational portion 63 has a dimension of length L₀greater than width W₀ and thickness T₀ smaller than the width W₀.Namely, a coupling between width-extensional mode and length-extensionalmode gets as small as it can be ignored, as a result of which, thequartz crystal resonator can vibrate in a single width-extensional mode,and also, a width-to-length ratio (W₀/L₀) has a value smaller than 0.7to provide the resonator with a small series resistance R₁ by increasingelectrode area of the vibrational portion. In addition, athickness-to-width ratio (T₀/W₀) has a value smaller than 0.85 toprovide the resonator with a small R₁ by increasing the intensity of anelectric field E_(x), These actual dimensions are, therefore, determinedby the requirement characteristics for the width-extensional mode quartzcrystal resonator.

In more detail, resonance frequency of the width-extensional mode quartzcrystal resonator is inversely proportional to width W₀, and it isalmost independent on such an other dimension as length L₀, thicknessT₀, connecting portions and supporting potions. Also, in order to obtaina width-extensional mode quartz crystal resonator with a frequency of 4MHz, the width W₀ is about 0.7 mm. Thus, the miniature width-extensionalmode quartz crystal resonator is provided with a frequency higher than 4MHz because resonance frequency of the resonator is inverselyproportional to the width W₀. Also, the resonator capable of vibratingin a single width-extensional mode can be obtained from the relation ofsaid dimensions.

Next, a value of a piezoelectric constant e₁₂ is described, which is ofgreat importance and necessary to excite a width-extensional mode quartzcrystal resonator of the present invention. The larger a value of thispiezoelectric constant e₁₂ becomes, the higher an electromechanicaltransformation efficiency becomes. For example, the piezoelectricconstant of the present invention e₁₂ is within a range of 0.095 C/m² to0.18 C/m² approximately in an absolute value. Also, the piezoelectricconstant e₁₂ in this embodiment can be calculated from the piezoelectricconstants e₁₁=0.171 C/m² and e₁₄=−0.0406 C/M² of quartz crystal. It iseasily understood that these are enough large values to obtain awidth-extensional mode quartz crystal resonator with a small capacitanceratio r, a small series resistance R₁ and a high quality factor Q.

Consequently, a quartz crystal oscillator comprising a quartz crystaloscillating circuit comprising the resonator of this embodiment having ahigh electromechanical transformation efficiency can be provided with asmall series resistance R₁ and a high quality factor Q. Also, the quartzcrystal oscillating circuit comprises an amplification circuitcomprising an amplifier at least and a feedback circuit comprising thequartz crystal resonator and capacitors at least. In detail, theamplification circuit comprises a CMOS inverter and a feedback resistorand the feedback circuit comprises a drain resistor, the resonator, acapacitor of a gate side and a capacitor of a drain side. Therefore, anoutput signal of the quartz crystal oscillator of this embodiment isused as a clock signal except time display of an electronic apparatus ofthe present invention.

Now, when an alternating current (AC) voltage is applied between theelectrodes 64 and 65 shown in FIG. 7 b, an electric field E_(x), occursalternately in the thickness direction, as shown by the arrow directionof the solid and broken lines. Consequently, the vibrational portion 63is capable of extending and contracting in the width direction.

FIG. 8 shows a cross-sectional view of a quartz crystal unitconstructing a quartz crystal oscillator, which constructs an electronicapparatus of the third embodiment of the present invention. The quartzcrystal unit 170 comprises a flexural mode, quartz crystal tuning forkresonator 70, a case 71 and a lid 72. In more detail, the resonator 70is mounted at a mounting portion 74 of the case 71 by conductiveadhesives 76 or solder. Also, the case 71 and the lid 72 are connectedthrough a connecting member 73. The resonator 70 in this embodiment isthe same resonator as the flexural mode, quartz crystal tuning forkresonator 10 described in detail in FIG. 4–FIG. 6. Also, in thisembodiment, circuit elements are connected at outside of the quartzcrystal unit to get a quartz crystal oscillator. Namely, only the quartzcrystal tuning fork resonator is housed in the unit and also, it ishoused in the unit in vacuum. In this embodiment, the quartz crystalunit of surface mounting type is shown, but the quartz crystal tuningfork resonator may be housed in tubular type.

In addition, a member of the case and the lid is ceramics or glass and ametal or glass, respectively, and a connecting member is a metal orglass with low melting point. Also, a relationship of the resonator, thecase and the lid described in this embodiment is applied to a quartzcrystal oscillator of the present invention which will be described inFIG. 9. In addition, instead of the quartz crystal tuning forkresonator, a width-extensional mode quartz crystal resonator or athickness shear mode quartz crystal resonator may be housed in the unit,

FIG. 9 shows a cross-sectional view of a quartz crystal oscillator,which constructs an electronic apparatus of the fourth embodiment of thepresent invention. The quartz crystal oscillator 190 comprises a quartzcrystal oscillating circuit, a case 91 and a lid 92. In this embodiment,circuit elements constructing the oscillating circuit are housed in aquartz crystal unit comprising a flexural mode, quartz crystal tuningfork resonator 90, the case 91 and the lid 92. Also, the quartz crystaloscillating circuit of this embodiment comprises an amplifier 98including a feedback resistor, the quartz crystal tuning fork resonator90, capacitors (not shown here) and a drain resistor (not shown here),and a CMOS inverter is used as the amplifier 98.

In addition, in this embodiment, the resonator 90 is mounted at amounting portion 94 of the case 91 by conductive adhesives 96 or solder.As described above, the amplifier 98 is housed in the quartz crystalunit and mounted at the case 91. Also, the case 91 and the lid 92 areconnected through a connecting member 93. The resonator 90 of thisembodiment is the same as the flexural mode, quartz crystal tuning forkresonators 10 described in detail in FIG. 4–FIG. 6. In this embodiment,though the resonator and the amplifier are housed in the same room, thepresent invention is not limited to this, for example, a room of thecase is divided into two rooms by a divided portion, and the amplifieris housed in one of the two rooms and the flexural mode, quartz crystaltuning fork resonator is housed in other room. Namely, the resonator andthe amplifier are housed in a separate room.

Likewise, in this embodiment, a piece of flexural mode, quartz crystaltuning fork resonator is housed in the unit, but the present inventionalso includes a quartz crystal unit having a plurality of flexural mode,quartz crystal tuning fork resonators, and at least two of the pluralityof resonators are connected electrically in parallel. In addition, theat least two resonators may be an individual resonator or may beindividual resonators that are formed integrally at each tuning basethrough a connecting portion. Also, a divided portion is constructedbetween the at least two resonators to prevent interference of vibrationeach other.

In addition, in order to construct a quartz crystal oscillator, twoelectrode terminals of the resonators are connected electrically to anamplifier, capacitors and resistors. In other words, a quartz crystaloscillating circuit is constructed and connected electrically so that anamplification circuit comprises a CMOS inverter and a feedback resistorand a feedback circuit comprises the flexural mode, quartz crystaltuning fork resonator, the drain resistor, the capacitor of a gate sideand the capacitor of a drain side.

In addition, an insulation material such as S_(i)O₂ may be constructedon obverse and reverse faces of the width W₁ and the width W₃ of thetuning fork tines to prevent a short circuit of between the electrodesof the sides and the grooves thereof, and the insulation material isformed by a spattering method or an evaporation method. Also, when atuning fork shape comprising tuning fork tines and a tuning fork base isformed by a photo-lithographic process and an etching process, cutportions may be also formed simultaneously at the tuning fork base.

Likewise, in the present embodiment, the flexural mode quartz crystalresonator of tuning fork type has two tuning fork tines, but embodimentof the present invention includes tuning fork tines more than two. Inaddition, the resonator of the present embodiment is housed in a package(unit) of surface mounting type comprising a case and a lid, but may behoused in a package of tubular type.

In addition, in the present embodiment, the grooves are constructed toinclude a portion of the central line of the tines, but the presentinvention is not limited to this, for example, the grooves may beconstructed with the portion of the central line of the tines and atboth sides thereof. In this case, a part width W₇ including the portionthe central line of the tines is less than 0.05 mm. Also, each groovewidth is less than 0.04 mm and a ratio (t₁/t) of groove thickness t₁,and tine thickness t is less than 0.79. By constructing the part widthW₇, the groove width and the thickness ratio like this, M₁ becomeslarger than M₂. Namely, the flexural mode, quartz crystal tuning forkresonator, capable of vibrating in a fundamental mode and having a highfrequency stability can be provided because the second overtone modevibration can be suppressed.

In addition, for the flexural mode, quartz crystal tuning fork resonatorconstructing the quartz crystal oscillators, which construct anelectronic apparatus of the present invention, the resonator isconstructed so that a capacitance ratio r₁, of a fundamental modevibration gets smaller than a capacitance ratio r₂ of a second overtonemode vibration, in order to obtain a frequency change of the fundamentalmode vibration larger than that of the second overtone mode vibration,versus the same change of a value of load capacitance C_(L). Namely, avariable range of a frequency of the fundamental mode vibration getswider than that of the second overtone mode vibration.

In more detail, for example, when C_(L)=18 pF and the C_(L) changes in 1pF, the frequency change of the fundamental mode vibration becomeslarger than that of the second overtone mode vibration because thecapacitance ratio r₁ is smaller than the capacitance ratio r₂.Therefore, there is a remarkable effect for the fundamental modevibration, such that the resonator can be provided with the frequencyvariable in the wide range, even when the value of load capacitanceC_(L) changes slightly. Accordingly, when a variation of the samefrequency is required, the number of capacitors which are used in thequartz crystal oscillators decreases because the frequency change versusload capacitance 1 pF becomes large, as compared with that of the secondovertone mode vibration. As a result, the low priced oscillators with anoutput signal of the fundamental mode vibration can be provided.

Moreover, capacitance ratios r₁ and r₂ of a flexural mode, quartzcrystal tuning fork resonator are given by r₁=C₀/C₁ and r₂=C₀/C₂,respectively, where C₀ is shunt capacitance in an electrical equivalentcircuit of the resonator, and C₁ and C₂ are, respectively, motionalcapacitance of a fundamental mode vibration and a second overtone modevibration in the electrical equivalent circuit of the resonator. Inaddition, the flexural mode, quartz crystal tuning fork resonator has aquality factor Q₁ for the fundamental mode vibration and a qualityfactor Q₂ for the second overtone mode vibration.

In more detail, the quartz crystal tuning fork resonator of thisembodiment is constructed so that the influence on resonance frequencyof the fundamental mode vibration by the shunt capacitance becomessmaller than that of the second overtone mode vibration by the shuntcapacitance, namely, so that it satisfies a relationship of r₁/2Q₁²<r₂/2Q₂ ². As a result, the flexural mode, quartz crystal tuning forkresonator, capable of vibrating in the fundamental mode and having ahigh frequency stability can be provided because the influence on theresonance frequency of the fundamental mode vibration by the shuntcapacitance becomes so extremely small as it can be ignored. Also, thepresent invention replaces r₁/2Q₁ ² with S₁ and r₂/2Q₂ ² with S₂,respectively, and here, the S₁ and S₂ are called “stable factor offrequency” of the fundamental mode vibration and the second overtonemode vibration. That is to say, the S₁ and S₂ are given by S₁=r₁/2Q₁ ²and S₂=r₂/2Q₂ ², respectively.

The above-described quartz crystal resonators are formed by at least onemethod of chemical, mechanical and physical methods. The mechanicalmethod, for example, uses a particle such as GC#1000 and the physicalmethod, for example, uses atom or molecule. Therefore, these methods arecalled “a particle method” here.

As described above, it will be easily understood that the electronicapparatus comprising the quartz crystal oscillator comprising the quartzcrystal oscillating circuit having the flexural mode, quartz crystaltuning fork resonator with novel shapes, the novel electrodeconstruction and excellent electrical characteristics, according to thepresent invention, may have the outstanding effects. Similar to this, itwill be easily understood that the electronic apparatus comprising thequartz crystal oscillator having the width-extensional mode quartzcrystal resonator with the novel cutting angle, according to the presentinvention, may have also the outstanding effect. In addition to this,while the present invention has been shown and described with referenceto preferred embodiments thereof, it will be understood by those skilledin the art that the changes in shape and electrode construction can bemade therein without departing from the spirit and scope of the presentinvention.

1. An electronic apparatus comprising: a display portion; and first andsecond quartz crystal oscillators comprised of first and second quartzcrystal oscillating circuits each having a quartz crystal resonator, anamplifier, a plurality of resistors, and a plurality of capacitors, amode of vibration of the quartz crystal resonator of the first quartzcrystal oscillating circuit being different from that of the quartzcrystal resonator of the second quartz crystal oscillating circuit;wherein the quartz crystal resonator of one of the first and secondquartz crystal oscillating circuits comprises a quartz crystal tuningfork resonator capable of vibrating in a flexural mode of an inversephase and having a fundamental mode of vibration and a second overtonemode of vibration, the quartz crystal tuning fork resonator beingelectrically connected to an amplification circuit having an amplifierand a feedback resistor and to a plurality of capacitors and a drainresistor of a feedback circuit having the quartz crystal tuning forkresonator, and the quartz crystal tuning fork resonator having a quartzcrystal tuning fork base, a plurality of quartz crystal tuning forktines connected to the quartz crystal tuning fork base, the quartzcrystal tuning fork tines having a first quartz crystal tuning fork tineand a second quartz crystal tuning fork tine, each of the first andsecond quartz crystal tuning fork tines having a first main surface anda second main surface opposite the first main surface, and at least onegroove having stepped portions formed in at least one of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines; wherein a merit value M₁ of the fundamental mode ofvibration of the quartz crystal tuning fork resonator is greater than amerit value M₂ of the second overtone mode of vibration thereof, themerit values M₁ and M₂ being defined by the ratios Q₁/r₁ and Q₂/r₂,respectively, where Q₁ and Q₂ represent a quality factor of thefundamental mode of vibration and the second overtone mode of vibration,respectively, of the quartz crystal tuning fork resonator and r₁ and r₂represent a capacitance ratio of the fundamental mode of vibration andthe second overtone mode of vibration, respectively, of the quartzcrystal tuning fork resonator; and wherein a ratio of an absolute valueof negative resistance −RL₁ of the fundamental mode of vibration of theamplification circuit and a series resistance R₁ of the fundamental modeof vibration is greater than that of an absolute value of negativeresistance −RL₂ of the second overtone mode of vibration of theamplification circuit and a series resistance R₂ of the second overtonemode of vibration.
 2. An electronic apparatus according to claim 1;wherein an output signal of the quartz crystal tuning fork resonator isa clock signal for operation of the electronic apparatus to display timeinformation at the display portion, the clock signal having anoscillation frequency of the fundamental mode of vibration of the quartzcrystal tuning fork resonator.
 3. An electronic apparatus according toclaim 2; wherein the amplifier of the amplification circuit comprises aCMOS inverter.
 4. An electronic apparatus according to claim 3; whereinthe at least one groove having stepped portions formed in at least oneof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines comprises a groove having steppedportions formed in each of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines so that a width ofthe groove formed in each of the first and second main surfaces of eachof the first and second quartz crystal tuning fork tines is greater thanor equal to a distance in the width direction of the groove measuredfrom an outer edge of the groove to an outer edge of the correspondingone of the first and second quartz crystal tuning fork tine.
 5. Anelectronic apparatus according to claim 4; wherein each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines has a central linear portion; and wherein the grooveformed in each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines is formed in thecentral linear portion of each of the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines so that aratio W₂/W is greater than 0.35 and less than 1, where W₂ represents awidth of the groove formed in the central linear portion of each of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines and W represents a width of each of the firstand second quartz crystal tuning fork tines.
 6. An electronic apparatusaccording to claim 5; wherein a length of at least one of the groovesformed in the central linear portions of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines is within a range of 40% to 80% of a length of each of the firstand second quartz crystal tuning fork tines.
 7. An electronic apparatusaccording to claim 5; wherein the groove formed in each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines is disposed opposite each other in a thicknessdirection of the first and second quartz crystal tuning fork tines. 8.An electronic apparatus according to claim 7; wherein each of the firstand second quartz crystal tuning fork tines has a side surfacecomprising an outer side surface; and further comprising a plurality offirst electrodes disposed in the grooves of the first and second quartzcrystal tuning fork tines and a plurality of second electrodes disposedon the outer side surfaces of the first and second quartz crystal tuningfork tines, the second electrodes of each of the first and second quartzcrystal tuning fork tines having an electrical polarity opposite to anelectrical polarity of the first electrodes of each of the first andsecond quartz crystal tuning fork tines.
 9. An electronic apparatusaccording to claim 8; wherein the first electrodes disposed in thegrooves of the first quartz crystal tuning fork tine are connected tothe second electrode disposed on the outer side surface of the secondquartz crystal tuning fork tine so that the first electrodes of thefirst quartz crystal tuning fork tine and the second electrode of thesecond quartz crystal tuning fork tine define a first electrodeterminal; and wherein the second electrode disposed on the outer sidesurface of the first quartz crystal tuning fork tine is connected to thefirst electrodes disposed in the grooves of the second quartz crystaltuning fork tine so that the second electrode of the first quartzcrystal tuning fork tine and the first electrodes of the second quartzcrystal tuning fork tine define a second electrode terminal.
 10. Anelectronic apparatus according to claim 9; wherein when a direct currentvoltage is applied between the first and second electrode terminals, adirection of an outer electric field generated between the secondelectrode disposed on the outer side surface of the first quartz crystaltuning fork tine and the first electrode disposed in one of the groovesopposite to the second electrode disposed on the outer side surface ofthe first quartz crystal tuning fork tine is the same as a direction ofan outer electric field generated between the second electrode disposedon the outer side surface of the second quartz crystal tuning fork tineand the first electrode disposed in one of the grooves opposite to thesecond electrode disposed on the outer side surface of the second quartzcrystal tuning fork tine; and wherein the directions of the outerelectric fields of the first and second quartz crystal tuning fork tinesare generally along an xaxis direction of the quartz crystal tuning forkresonator.
 11. An electronic apparatus according to claim 10; whereinthe quartz crystal resonator of one of the first and second quartzcrystal oscillating circuits comprises one of a widthextensional modequartz crystal resonator capable of vibrating in a widthextensional modeand a thickness shear mode quartz crystal resonator capable of vibratingin a thickness shear mode.
 12. An electronic apparatus according toclaim 10; wherein a length of at least one of the grooves formed in thecentral linear portions of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines is within a rangeof 40% to 80% of a length of each of the first and second quartz crystaltuning fork tines.
 13. An electronic apparatus according to claim 10;wherein a series resistance R₁ of the fundamental mode of vibration ofthe quartz crystal tuning fork resonator is less than a seriesresistance R₂ of the second overtone mode of vibration thereof; andwherein a capacitance ratio r₁ of the fundamental mode of vibration ofthe quartz crystal tuning fork resonator is less than a capacitanceratio r₂ of the second overtone mode of vibration thereof.
 14. Anelectronic apparatus according to claim 10; further comprising thequartz crystal tuning fork resonator having a piezoelectric constant e₁₂to drive the quartz crystal tuning fork resonator; wherein thepiezoelectric constant e₁₂ of the quartz crystal tuning fork resonatoris within a range of 0.095 c/m² to 0.18 c/m² in the absolute value. 15.An electronic apparatus according to claim 4; wherein a spacedapartdistance between the first and second quartz crystal tuning fork tinesis greater than or equal to a width of at least one of the groovesformed in the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines.
 16. An electronic apparatusaccording to claim 15; wherein a width W₂ of at least one of the groovesformed in the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines is within a range of 0.03 mm to0.12 mm; and wherein a ratio W₂/W is greater than 0.35 and less than 1,where W represents a width of each of the first and second quartzcrystal tuning fork tines.
 17. An electronic apparatus according toclaim 16; wherein a length of at least one of the grooves formed in thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines is within a range of 40% to 80% of a length ofeach of the first and second quartz crystal tuning fork tines.
 18. Anelectronic apparatus according to claim 4; wherein the groove formed ineach of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines has a first outer edge and asecond outer edge opposite to the first outer edge in the widthdirection of the corresponding one of the first and second quartzcrystal tuning fork tines; wherein each of the first and second quartzcrystal tuning fork tines has a first outer edge and a second outer edgeopposite to the first outer edge; wherein a first part of each of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines is formed between the first outer edge of thecorresponding groove and the first outer edge of the corresponding oneof the first and second quartz crystal tuning fork tines; wherein asecond part of each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines is formed between thesecond outer edge of the corresponding groove and the second outer edgeof the corresponding one of the first and second quartz crystal tuningfork tines; and wherein an insulation material is disposed on each ofthe first and second parts of the first and second main surfaces of eachof the first and second quartz crystal tuning fork tines.
 19. Anelectronic apparatus according to claim 18; wherein the insulationmaterial comprises SiO₂.
 20. An electronic apparatus according to claim4; wherein the quartz crystal tuning fork base connected to the firstand second quartz crystal tuning fork tines has cut portions.
 21. Anelectronic apparatus according to claim 1; wherein the quartz crystalresonator of one of the first and second quartz crystal oscillatingcircuits comprises one of a widthextensional mode quartz crystalresonator capable of vibrating in a width-extensional mode and athickness shear mode quartz crystal resonator capable of vibrating in athickness shear mode.
 22. An electronic apparatus according to claim 21;wherein the at least one groove having stepped portions is formed ineach of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines so that a width of at least oneof the grooves formed in the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines is greater than orequal to a distance in the width direction of the groove measured froman outer edge of the groove to an outer edge of the quartz crystaltuning fork tine in which the groove is formed; and wherein a length ofat least one of the grooves formed in the first and second main surfacesof each of the first and second quartz crystal tuning fork tines iswithin a range of 40% to 80% of a length of each of the first and secondquartz crystal tuning fork tines.
 23. An electronic apparatus accordingto claim 22; wherein a spaced-apart distance between the first andsecond quartz crystal tuning fork tines is within a range of 0.05 mm to0.35 mm and is greater than or equal to a width of at least one of thegrooves formed in the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines.
 24. An electronicapparatus according to claim 2; wherein the at least one groove havingstepped portions is formed in each of the first and second main surfacesof each of the first and second quartz crystal tuning fork tines so thata width of at least one of the grooves formed in the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines is greater than or equal to a distance in the width direction ofthe groove measured from an outer edge of the groove to an outer edge ofthe quartz crystal tuning fork tine in which the groove is formed; andwherein a length of at least one of the grooves formed in the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines is within a range of 40% to 80% of a length of each ofthe first and second quartz crystal tuning fork tines.
 25. An electronicapparatus according to claim 2; wherein the quartz crystal resonator ofone of the first and second quartz crystal oscillating circuitscomprises one of a width-extensional mode quartz crystal resonatorcapable of vibrating in a widthextensional mode and a thickness shearmode quartz crystal resonator capable of vibrating in a thickness shearmode; and further comprising a case for housing the quartz crystalresonator and a lid for covering an open end of the case.
 26. Anelectronic apparatus according to claim 25; wherein a width W₂ of the atleast one groove formed in at least one of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines is within a range of 0.03 mm to 0.12 mm, wherein a ratio W₂/W isgreater than 0.35 and less than 1, where W represents a width of each ofthe first and second quartz crystal tuning fork tines; and wherein alength of the at least one groove formed in at least one of the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines is within a range of 40% to 80% of a length of each ofthe first and second quartz crystal tuning fork tines.
 27. An electronicapparatus according to claim 26; wherein a spacedapart distance betweenthe first and second quartz crystal tuning fork tines is greater than orequal to a width of the at least one groove formed in at least one ofthe first and second main surfaces of each of the first and secondquartz crystal tuning fork tines.
 28. An electronic apparatus accordingto claim 27; wherein a series resistance R₁ of the fundamental mode ofvibration of the quartz crystal tuning fork resonator is less than aseries resistance R₂ of the second overtone mode of vibration thereof;and wherein a capacitance ratio r₁ of the fundamental mode of vibrationof the quartz crystal tuning fork resonator is less than a capacitanceratio r₂ of the second overtone mode of vibration thereof.
 29. Anelectronic apparatus comprising: a display portion; and first and secondquartz crystal oscillators comprised of first and second quartz crystaloscillating circuits each having a quartz crystal resonator, anamplifier, a plurality of resistors, and a plurality of capacitors, amode of vibration of the quartz crystal resonator of the first quartzcrystal oscillating circuit being different from that of the quartzcrystal resonator of the second quartz crystal oscillating circuit;wherein the quartz crystal resonator of one of the first and secondquartz crystal oscillating circuits comprises one of a width-extensionalmode quartz crystal resonator capable of vibrating in a widthextensionalmode and a thickness shear mode quartz crystal resonator capable ofvibrating in a thickness shear mode; wherein the quartz crystalresonator of one of the first and second quartz crystal oscillatingcircuits comprises a quartz crystal tuning fork resonator capable ofvibrating in a flexural mode of an inverse phase and having afundamental mode of vibration and a second overtone mode of vibration,the quartz crystal tuning fork resonator being electrically connected toan amplification circuit having a CMOS inverter and a feedback resistorand to a plurality of capacitors and a drain resistor of a feedbackcircuit having the quartz crystal tuning fork resonator, and the quartzcrystal tuning fork resonator having a quartz crystal tuning fork baseand a plurality of quartz crystal tuning fork tines connected to thequartz crystal tuning fork base, the quartz crystal tuning fork tineshaving a first quartz crystal tuning fork tine and a second quartzcrystal tuning fork tine, each of the first and second quartz crystaltuning fork tines having a first main surface and a second main surfaceopposite the first main surface; wherein a merit value M₁ of thefundamental mode of vibration of the quartz crystal tuning forkresonator is greater than a merit value M₂ of the second overtone modeof vibration thereof, the merit values M₁ and M₂ being defined by theratios Q₁/r₁ and Q₂/r₂, respectively, where Q₁ and Q₂ represent aquality factor of the fundamental mode of vibration and the secondovertone mode of vibration, respectively, of the quartz crystal tuningfork resonator and r_(1 land r) ₂ represent a capacitance ratio of thefundamental mode of vibration and the second overtone mode of vibration,respectively, of the quartz crystal tuning fork resonator; wherein aratio of an absolute value of negative resistance −RL₁ of thefundamental mode of vibration of the amplification circuit and a seriesresistance R₁ of the fundamental mode of vibration is greater than thatof an absolute value of negative resistance −RL₂ of the second overtonemode of vibration of the amplification circuit and a series resistanceR₂ of the second overtone mode of vibration; and wherein an outputsignal of the quartz crystal tuning fork resonator is a clock signal foroperation of the electronic apparatus to display time information at thedisplay portion, the clock signal having an oscillation frequency of thefundamental mode of vibration of the quartz crystal tuning forkresonator.
 30. An electronic apparatus according to claim 29; wherein aseries resistance R₁ of the fundamental mode of vibration of the quartzcrystal tuning fork resonator is less than a series resistance R₂ of thesecond overtone mode of vibration thereof; and wherein a capacitanceratio r₁ of the fundamental mode of vibration of the quartz crystaltuning fork resonator is less than a capacitance ratio r₂ of the secondovertone mode of vibration thereof.
 31. An electronic apparatusaccording to claim 30; wherein a stable factor S₁ of the fundamentalmode of vibration of the quartz crystal tuning fork resonator and astable factor S₂ of the second overtone mode of vibration thereof aredefined by r₁/2Q₁ ² and r₂/2Q₂ ², respectively; and wherein S₁ is lessthan S₂.
 32. An electronic apparatus according to claim 31; wherein aratio of an amplification rate α₁ of the fundamental mode of vibrationand an amplification rate α₂ of the second overtone mode of vibration ofthe amplification circuit is greater than that of a feedback rate β₂ ofthe second overtone mode of vibration and a feedback rate β₁ of thefundamental mode of vibration of the feedback circuit and a product ofthe amplification rate α₁ and the feedback rate β₁ of the fundamentalmode of vibration is greater than
 1. 33. An electronic apparatusaccording to claim 32; wherein the feedback circuit having the quartzcrystal tuning fork resonator comprises a capacitor of a gate sidehaving a capacitance C_(g) and a capacitor of a drain side having acapacitance C_(d); and wherein a load capacitance C_(L) of thecapacitors is less than 18 pF, where C_(L) is defined byC_(g)C_(d)/(C_(g)+C_(d)).
 34. An electronic apparatus according to claim33; wherein at least one groove having a plurality of stepped portionsis formed in at least one of the first and second main surfaces of eachof the first and second quartz crystal tuning fork tines.
 35. Anelectronic apparatus according to claim 34; wherein the at least onegroove having a plurality of stepped portions comprises a groove havinga plurality of stepped portions formed in each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines so that a ratio W₂/W is greater than 0.35 and less than 1, whereW₂ represents a width of at least one of the grooves formed in the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines and W represents a width of each of the first andsecond quartz crystal tuning fork tines; and wherein a length of atleast one groove having the ratio W₂/W greater than 0.35 and less than 1is within a range of 40% to 80% of a length of each of the first andsecond quartz crystal tuning fork tines.
 36. An electronic apparatusaccording to claim 33; further comprising the quartz crystal tuning forkresonator having a piezoelectric constant e₁₂ to drive the quartzcrystal tuning fork resonator; wherein the piezoelectric constant e₁₂ ofthe quartz crystal tuning fork resonator is within a range of 0.095 c/m²to 0.18 c/m² in the absolute value.
 37. An electronic apparatusaccording to claim 33; wherein a spacedapart distance between the firstand second quartz crystal tuning fork tines is within a range of 0.05 mmto 0.35 mm; and wherein the merit value M₂ for the second overtone modeof vibration of the quartz crystal tuning fork resonator is less than 30so that the second overtone mode of vibration thereof is suppressed. 38.An electronic apparatus according to claim 37; wherein a groove having aplurality of stepped portions is formed in each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines so that a width of at least one of the grooves formed in the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines is greater than or equal to a distance in the widthdirection of the groove measured from an outer edge of the groove to anouter edge of the corresponding quartz crystal tuning fork tine in whichthe groove is formed; and wherein the spaced-apart distance between thefirst and second quartz crystal tuning fork tines is greater than orequal to the width of at least one of the grooves formed in the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines.
 39. An electronic apparatus according to claim 38;wherein a length of at least one of the grooves formed in the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines is within a range of 40% to 80% of a length of each ofthe first and second quartz crystal tuning fork tines.
 40. An electronicapparatus according to claim 33; wherein a spacedapart distance betweenthe first and second quartz crystal tuning fork tines is within a rangeof 0.05 mm to 0.35 mm; and wherein the merit value M₁ for thefundamental mode of vibration of the quartz crystal tuning forkresonator is greater than 65 so that a high frequency stability for thefundamental mode of vibration thereof is obtained.
 41. An electronicapparatus according to claim 33; wherein a groove having a plurality ofstepped portions is formed in each of the first and second main surfacesof each of the first and second quartz crystal tuning fork tines so thata ratio W₂/W is greater than 0.35 and less than 1, where W₂ represents awidth of at least one of the grooves formed in the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines and W represents a width of each of the first and second quartzcrystal tuning fork tines; wherein a first electrode is disposed on aside surface of one of the first and second quartz crystal tuning forktines and a second electrode having an electrical polarity differentfrom that of the first electrode is disposed on one of the steppedportions of at least one of the grooves formed in the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines, the first electrode disposed on the side surface of one of thefirst and second quartz crystal tuning fork tines being opposite thesecond electrode disposed on one of the stepped portions of at least oneof the grooves formed in the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines; and wherein alength of at least one groove having the ratio W₂/W greater than 0.35and less than 1 and having the stepped portion on which the secondelectrode opposite the first electrode is disposed is within a range of40% to 80% of a length of each of the first and second quartz crystaltuning fork tines.
 42. An electronic apparatus comprising: a displayportion; and first and second quartz crystal oscillators comprised offirst and second quartz crystal oscillating circuits each having aquartz crystal resonator, an amplifier, a plurality of resistors, and aplurality of capacitors, a mode of vibration of the quartz crystalresonator of the first quartz crystal oscillating circuit beingdifferent from that of the quartz crystal resonator of the second quartzcrystal oscillating circuit; wherein the quartz crystal resonator of oneof the first and second quartz crystal oscillating circuits comprises athickness shear mode quartz crystal resonator capable of vibrating in athickness shear mode; wherein the quartz crystal resonator of one of thefirst and second quartz crystal oscillating circuits comprises a quartzcrystal tuning fork resonator capable of vibrating in a flexural mode ofan inverse phase and having a fundamental mode of vibration and a secondovertone mode of vibration, the quartz crystal tuning fork resonatorbeing electrically connected to an amplification circuit having a CMOSinverter and a feedback resistor and to a plurality of capacitors and adrain resistor of a feedback circuit having the quartz crystal tuningfork resonator, and the quartz crystal tuning fork resonator having aquartz crystal tuning fork base and a plurality of quartz crystal tuningfork tines connected to the quartz crystal tuning fork base, the quartzcrystal tuning fork tines having a first quartz crystal tuning fork tineand a second quartz crystal tuning fork tine, each of the first andsecond quartz crystal tuning fork tines having a first main surface anda second main surface opposite the first main surface; wherein a meritvalue M₁ of the fundamental mode of vibration of the quartz crystaltuning fork resonator is greater than a merit value M₂ of the secondovertone mode of vibration thereof, the merit values M₁ and M₂ beingdefined by the ratios Q₁/r₁ and Q₂/r₂, respectively, where Q₁ and Q₂represent a quality factor of the fundamental mode of vibration and thesecond overtone mode of vibration, respectively, of the quartz crystaltuning fork resonator and r₁ and r₂ represent a capacitance ratio of thefundamental mode of vibration and the second overtone mode of vibration,respectively, of the quartz crystal tuning fork resonator; wherein aratio of an amplification rate α₁ of the fundamental mode of vibrationand an amplification rate α₂ of the second overtone mode of vibration ofthe amplification circuit is greater than that of a feedback rate B₂ ofthe second overtone mode of vibration and a feedback rate B₁ of thefundamental mode of vibration of the feedback circuit and a product ofthe amplification rate α₁ and the feedback rate B₁ of the fundamentalmode of vibration is greater than 1; and wherein an output signal of thequartz crystal oscillating circuit comprising the quartz crystal tuningfork resonator is a clock signal for operation of the electronicapparatus to display time information at the display portion, the clocksignal having an oscillation frequency of the fundamental mode ofvibration of the quartz crystal tuning fork resonator.
 43. An electronicapparatus according to claim 42; wherein a series resistance R₁ of thefundamental mode of vibration of the quartz crystal tuning forkresonator is less than a series resistance R₂ of the second overtonemode of vibration thereof, a capacitance ratio r₁ of the fundamentalmode of vibration of the quartz crystal tuning fork resonator being lessthan a capacitance ratio r₂ of the second overtone mode of vibrationthereof; and wherein when a stable factor S₁ of the fundamental mode ofvibration of the quartz crystal tuning fork resonator and a stablefactor S₂ of the second overtone mode of vibration thereof are definedby r₁/2Q₁ ² and r₂/2Q₂ ², respectively, S₁ is less than S₂.
 44. Anelectronic apparatus according to claim 42; wherein a cutting angle ofthe quartz crystal tuning fork resonator is within a range of ZYw(0° to10°); and wherein a piezoelectric constant e₁₂ of the quartz crystaltuning fork resonator is within a range of 0.095 C/m² to 0.18 C/m² inthe absolute value.
 45. An electronic apparatus according to claim 42;wherein each of the first and second main surfaces of each of the firstand second quartz crystal tuning fork tines has a central linearportion; wherein a groove having a plurality of stepped portions isformed in each of the central linear portions of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines so that a width of the groove is greater than or equal to adistance in the width direction of the groove measured from an outeredge of the groove to an outer edge of the quartz crystal tuning forktine in which the groove is formed; wherein a first electrode isdisposed on a side surface of one of the first and second quartz crystaltuning fork tines and a second electrode having an electrical polaritydifferent from that of the first electrode is disposed on one of thestepped portions of at least one of the grooves formed in the centrallinear portions of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines, the first electrodedisposed on the side surface of one of the first and second quartzcrystal tuning fork tines being opposite the second electrode disposedon one of the stepped portions of at least one of the grooves formed inthe central linear portions of the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines; andwherein a length of at least one groove having the width and the steppedportion on which the second electrode opposite the first electrode isdisposed is within a range of 40% to 80% of a length of each of thefirst and second quartz crystal tuning fork tines.
 46. An electronicapparatus according to claim 42; wherein each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines has a central linear portion; wherein a groove having a pluralityof stepped portions is formed in each of the central linear portions ofthe first and second main surfaces of each of the first and secondquartz crystal tuning fork tines so that a ratio W₂/W is greater than0.35 and less than 1, where W₂ represents a width of at least one of thegrooves formed in the central linear portions of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines and W represents a width of each of the first and second quartzcrystal tuning fork tines; wherein a first electrode is disposed on aside surface of one of the first and second quartz crystal tuning forktines and a second electrode having an electrical polarity differentfrom that of the first electrode is disposed on one of the steppedportions of at least one of the grooves formed in the central linearportions of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines, the first electrode disposed onthe side surface of one of the first and second quartz crystal tuningfork tines being opposite the second electrode disposed on one of thestepped portions of at least one of the grooves formed in the centrallinear portions of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines; and wherein a lengthof at least one groove having the ratio W₂/W greater than 0.35 and lessthan 1 and having the stepped portion on which the second electrodeopposite the first electrode is disposed is within a range of 40% to 80%of a length of each of the first and second quartz crystal tuning forktines.
 47. An electronic apparatus according to claim 42; wherein agroove having a plurality of stepped portions is formed in each of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines so that a width of the groove is greater thanor equal to a distance in the width direction of the groove measuredfrom an outer edge of the groove to an outer edge of the quartz crystaltuning fork tine in which the groove is formed; and wherein aspaced-apart distance between the first and second quartz crystal tuningfork tines is within a range of 0.05 mm to 0.35 mm and is greater thanor equal to the width of at least one of the grooves formed in the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines.
 48. An electronic apparatus according to claim 47;wherein a length of the groove having a plurality of stepped portionsformed in each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines is within a range of40% to 80% of a length of each of the first and second quartz crystaltuning fork tines.